2n+32=2/9n

Solution for 2n+32=2/9n equation:

2n+32=2/9n

We move all terms to the left:

2n+32-(2/9n)=0


Domain of the equation: 9n)!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

2n-(+2/9n)+32=0

We get rid of parentheses

2n-2/9n+32=0

We multiply all the terms by the denominator


2n*9n+32*9n-2=0

Wy multiply elements

18n^2+288n-2=0

a = 18; b = 288; c = -2;
Δ = b2-4ac
Δ = 2882-4·18·(-2)
Δ = 83088
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{83088}=\sqrt{144*577}=\sqrt{144}*\sqrt{577}=12\sqrt{577}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(288)-12\sqrt{577}}{2*18}=\frac{-288-12\sqrt{577}}{36}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(288)+12\sqrt{577}}{2*18}=\frac{-288+12\sqrt{577}}{36}
$